μ ∈ R — mean (location)|
In probability theory and statistics, the normal-exponential-gamma distribution (sometimes called the NEG distribution) is a three-parameter family of continuous probability distributions. It has a location parameter , scale parameter and a shape parameter .
Probability density function
The probability density function (pdf) of the normal-exponential-gamma distribution is proportional to
where D is a parabolic cylinder function.
As for the Laplace distribution, the pdf of the NEG distribution can be expressed as a mixture of normal distributions,
where, in this notation, the distribution-names should be interpreted as meaning the density functions of those distributions.
The distribution has heavy tails and a sharp peak at and, because of this, it has applications in variable selection.
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. (December 2010)